Offsetting operations in solid modelling
Computer Aided Geometric Design
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SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Blending and offsetting solid models (cad/cam, computational geometry, representations, curves, surfaces, approximation)
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Theoretical Computer Science - Topology in computer science
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
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SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
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SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
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Discrete & Computational Geometry
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Stability of curvature measures
SGP '09 Proceedings of the Symposium on Geometry Processing
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Proceedings of the twenty-sixth annual symposium on Computational geometry
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It has been observed for a long time that the operation consisting of offsetting a solid by a quantity r and then offsetting its complement by d r produces, in some cases, a new solid with the same topology but with a smooth boundary. While this fact has been widely used in Computer Aided Geometric Design or in the field of image processing, we provide here for the first time a tight and robust condition that guarantees the smoothness of the new solid and gives a lower bound on its reach (distance to the medial axis). This condition is based on the general properties of the distance function to a compact set and relies on the recently introduced critical function and μ-reach.